Practice Test 18 - Algebra 2

20 questions. Answer them in any order, then submit to see your score and every explanation.

Start practice test

1. Graph the trigonometric function $r(x)=\sin(x)-2$ showing its amplitude, midline, and period.
2. Solve the system by both substitution and elimination (they should give the same result): $\begin{cases} x - y = 2\\ 2x + y = 10 \end{cases}$ What is the solution $(x, y)$?
3. A bike rental shop charges a one-time service fee of $12 plus $5 per hour. 1) Write an equation for the total cost $C$ (dollars) in terms of hours rented $h$ (hours). 2) Then choose the best axes labels and reasonable scales to graph the relationship for $0\le h\le 10$. Which choice gives both the correct equation and an appropriate graph setup?
4. Function $f$ is linear and given by $f(x) = -4x + 7$. Function $g$ is represented by the table. \begin{center} \begin{tabular}{c|c} $x$ & $g(x)$ \\\hline $0$ & $2$ \\ $1$ & $5$ \\ $2$ & $8$ \\ $3$ & $11$ \\ \end{tabular} \end{center} Which function has the greater slope (rate of change)?
5. The balance in an account is modeled by $A(t)=1200(1.05)^t$, where $A$ is the amount of money in dollars and $t$ is time in years. What is the annual growth rate as a percent?
6. A device's battery charge is measured every 30 minutes. Interval $n$: 0, 1, 2, 3 Charge $C(n)$ (%): 100, 85, 72.25, 61.4125 Identify the constant percent rate of change per 30-minute interval and classify as growth or decay.​​
7. Consider $K(x)=\frac{(x-3)(x+2)}{(x-3)}.$ If you view $(x-3)$ as a single entity appearing in both numerator and denominator, which statement best describes the structure (for $x\ne 3$) without focusing on full simplification as the main goal?
8. Consider the polynomial $P(x) = x^6 - 64$. When factored completely over the complex numbers, how many distinct linear factors does $P(x)$ have?
9. Use the polynomial division algorithm to write $\frac{x^4-3x^2+5}{x^2+1}$ in the form $q(x)+\frac{r(x)}{x^2+1}$, where $\deg(r)<2$.
10. Identify the structure (perfect square trinomial) and rewrite the expression in squared form: $x^2-10x+25$
11. Two students define sequences differently. Student A: $x_n = 2n + 1$ for $n \geq 1$. Student B: $y_1 = 3$ and $y_n = y_{n-1} + 2$ for $n \geq 2$. Which statement about these sequences as functions is most accurate?
12. For the logarithmic function $q(x)=2\ln(x)+1$, which statement correctly gives the domain, vertical asymptote, and end behavior?​
13. A bookstore's reward points increase by 15 points each week. In week 1, a customer has 40 points. Model the total points after $n$ weeks as a function with integer domain $n \ge 1$ by writing both a recursive formula and an explicit formula for the sequence.
14. A concert venue charges $18 per ticket and has a fixed rental cost of $250 for the night. Let $q$ be the number of tickets sold. Revenue is $R=18q$ and cost is $C=250+6q$ (staffing depends on attendance). Create an equation for profit $P$ in terms of $q$, and choose appropriate axes labels and a reasonable scale to graph profit for $0 \le q \le 100$.
15. Identify zeros and their multiplicities for $p(x)=(x-5)(x+1)^2(x-2)^2,$ then determine the end behavior and whether the graph crosses or touches at each zero.
16. Recognize the structure as a sum of cubes and factor: $8x^3 + 27$
17. Graph $f(x)=\frac{x^2-4}{x-3}$ by identifying zeros, the vertical asymptote, and the oblique (slant) asymptote. Choose the option with the correct set of features.
18. Use the Rational Zeros Theorem to list all possible rational zeros of $P(x)=4x^4-5x^3-8x^2+3x+6.$
19. Use the inverse relationship to simplify $2^{\log_2(17)}$ (note: the argument $17>0$).
20. Write an expression for $f^{-1}(x)$ given $f(x)=\dfrac{x-4}{3}$.

Practice tests